Measures with positive Lyapunov exponent and conformal measures in rational dynamics

DOI10.1090/S0002-9947-2012-05366-9zbMath1267.37042arXiv0804.3753MaRDI QIDQ2884387

Neil B. Dobbs

Publication date: 29 May 2012

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0804.3753

zbMATH Keywords

Lyapunov exponentrational mapsconformal measuresregularly returning cylinder

Mathematics Subject Classification ID

Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25)

Related Items (10)

Yet another induction scheme for non-uniformly expanding transformations ⋮ Sensitive dependence of geometric Gibbs states at positive temperature ⋮ High-order phase transitions in the quadratic family ⋮ Low-temperature phase transitions in the quadratic family ⋮ Geometric pressure for multimodal maps of the interval ⋮ On cusps and flat tops ⋮ STOCHASTIC POTENTIALS OF INTERMITTENT MAPS ⋮ Dimension theory for multimodal maps ⋮ Knobbly but nice ⋮ Pesin theory and equilibrium measures on the interval

Cites Work

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• A connecting lemma for rational maps satisfying a no-growth condition
• On the Bernoulli property for rational maps
• Some properties of absolutely continuous invariant measures on an interval
• ON THERMODYNAMICS OF RATIONAL MAPS. II: NON-RECURRENT MAPS
• Equality of pressures for rational functions
• Statistical properties of topological Collet–Eckmann maps
• Ergodic theory of equilibrium states for rational maps

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